RO  EN
IMI/Publicaţii/BASM/Ediţii/BASM n.3(85), 2017/

Semi-symmetric isotopic closure of some group varieties and the corresponding identities

Authors: Halyna Krainichuk, Olena Tarkovska

Abstract

Four families of pairwise equivalent identities are given and analyzed. Every identity from each of these families defines one of the following varieties: 1)~the semi-symmetric isotopic closure of the variety of all Boolean groups; 2)~the semi-symmetric isotopic closure of the variety of all Abelian groups; 3)~the semi-symmetric isotopic closure of the variety of all groups; 4)~the variety of all semi-symmetric quasigroups. It is proved that these varieties are different and form a chain. Quasigroups belonging to these varieties are described. In particular, quasigroups from 1) and 2) varieties are medial and in addition, they are either groups or non-commutative semi-symmetric quasigroups.

V. Stus Donetsk National University
Department of mathematical analysis
and differential equations
21000 Vinnytsia, Ukraine
E-mail: ,

Fulltext

Adobe PDF document0.19 Mb